While you're listening to the awesome music in the previous post, I'd like to address this question just a little bit. I think it's one of the most common preflop leaks in SH LHE players from low to highstakes. At least I think now, but I haven't done any calculations whatsoever, so maybe it's one of my biggest leaks, we'll see.
So do you 3bet A2o vs a regular BU opener? I sure do. I've heard a lot of arguments against it, and very few for it. Let's see those arguments, so that we could tear them apart and see if they're wrong or right.
A few of those arguments (if you have any further, let me know, so that we can elaborate on them too):
- A2o is a dominated hand
- if we 3bet with A2o, we either win a small pot, or lose a big one with it (I think Deathdonkey said that for raggy aces)
- A2o will be in the no men's land on the turn unimproved, we usually have to check/fold or check/crying calldown with it, which sucks
- (our range won't be balanced, it will be too A-high heavy - that one I made up, but for me it's the only reasonable argument against it)
These are all that I could think of, but if you have any, let me know. So let's get into it:
Against my own BU range:
Holdem, Generic syntax
PLAYER_1 $ORBU
PLAYER_2 A2$o
13068304128 trials (exhaustive)
| $ORBU | A2$o |
|---|
| Equity % | 51,2244% | 48,7756% |
| Wins Hi % | 47,7664% | 45,3177% |
| Ties Hi % | 6,9159% | 6,9159% |
| Wins Hi Count | 6242261895 | 5922256311 |
| Ties Hi Count | 903785922 | 9037859 |
Ok, so first off it seems pretty weird that I don't want to 3bet a hand with 49% equity, but I want to 3bet a hand like T9s that has 46%. (Of course HCEQ is not everything, it's more close to nothing than everything.)
Doing a quick HCEV calculation (assuming Villain doesn't cap anything and BB always folds): 0.49*4.5 - 0.51*2.5 = 0.93 SB
So that ~1 SB has to be lost either by not realizing our equity or by RIO and other factors, like BB being involved in the hand.
True Equity calculation:
Let's take an easy example: we bet the flop, Villain calls, we check the turn planning to check/fold if we don't have the appropriate equity to continue. The pot odds would be 5.5:1, so we have to have 15.38 equity to continue. Since we usually have to call down here, and can't continue drawing, we should use more like 5.5:2 = 26,67%. Since we can call/fold sometimes, let's say 25%. What will our average equity be, when we have either more than 25% equity on the turn, or 0. I made a quick PQL script for it, I'll write about that in a later post. Now just accept, that our preflop equity if we always check/fold the turn below 25% equity is around
46.3%. That still doesn't sounds bad, considering we should have around 43-44% equity to 3bet from the SB. Also this script doesn't take into account, that most of the time we're also gonna make him fold equity (or even a better hand), therefore I believe our actual True Equity should be higher, or at least even to our HCEQ. That didn't change anything, let's see the RIO stuff.
Reversed Implied Odds:
That's a yucky one. I'm not certainly sure how to calculate that exactly, but I'd say against a weak range that contains a lot of rubbish hands that won't make that much valueraising hands, I don't think there is a RIO of 1 small bet. In my mind that would basically mean that the opponent plays incorrectly (by not bluffing or vraising thin enough), which we can exploit in theory, so a RIO of 1 SB seems extremely high to me. When I did some RIO calculations in the past, I got around .2-.25 BB maximum to RIO, I'm not sure if it was exhaustive enough, but I got the feel that it won't ever be that high.
About the domination
The hands this hand is dominated by but A6o is not, are hands that most usually split with our hand (or we make them fold by the river):
Holdem, Generic syntax
PLAYER_1 A4$o
PLAYER_2 A2$o
184928832 trials (exhaustive)
| A4$o | A2$o |
|---|
| Equity % | 53,3909% | 46,6091% |
| Wins Hi % | 28,4576% | 21,6758% |
| Ties Hi % | 49,8667% | 49,8667% |
| Wins Hi Count | 52626276 | 40084728 |
| Ties Hi Count | 92217828 | 92217828 |
As you can see these hands will split the pot almost 50% of the time. Also in these situations we will have the advantage of initiative and we can barrel them off of these hands quite easily, so I find that argument very invalid. (Also the chance of him having the A and the board to have an A on it is pretty low.)
About balance
Now here comes the tricky part... I think I convinced myself well enough, so that I could say fuck balance in this spot, but let's still take a look at it. Let's assume two different 3betting ranges: one we put together with a friend of mine for these spots, and the other one with all the aces included in it:
Range 1: 22+,A2s+,K7s+,Q8s+,J8s+,T8s+,97s+,87s,76s,A6o+,K9o+,QTo+,JTo,T9o
Range 2: 22+,A2s+,K7s+,Q8s+,J8s+,T8s+,97s+,87s,76s,A2o+,K9o+,QTo+,JTo,T9o
So if we take a look at how the BU openrange shares against these 2 ranges on an A hi dry board (let's say A83r for the extreme).
ORBU vs Range 1: range asymmetry is on our side with 56.6%
ORBU vs Range 2: range asymmetry is on our side (LDO) with 59% equity.
Now range on range it's quite a lot of difference that 2.4%, however I believe that our initial range is maybe a bit tight, and with the offsuit aces included, we maybe can include some more suited/connected stuff in there (Q7s, 98o maybe, Q9o, J9o, something like that), and make peace once again. Also I still don't hate that 59% percent in itself, although seems a bit highish.
So that would conclude why I 3bet A2o BU vs SB, hope I could convince you to do so (although I'm fine if you don't :P), and I hope you liked the analysis.
Any feedback or comment is appreciated. Cheers.
